How the percentage calculator works
"Percent" means "per hundred", so every percentage problem is a ratio scaled by 100. The calculator picks the right formula for the question you choose:
Percent = Part ÷ Whole × 100
Whole = Part ÷ (Percent ÷ 100)
Percent change compares a new value with an old one: (new − old) ÷ |old| × 100. A positive result is an increase and a negative one is a decrease. It is undefined when the old value is 0.
Percent difference compares two values when neither is the "original": |X − Y| divided by their average, × 100. It gives the same answer whichever order you enter them.
Results are shown rounded to up to 6 significant decimals; the step-by-step box shows the exact calculation.
Worked example
A $80 jacket is 15% off. The discount is 15 ÷ 100 × 80 = $12, so you pay 80 × (1 − 0.15) = $68.
80 decreased by 15% = 80 × 0.85 = 68
If your rent goes from $1,600 to $1,720, the percent change is (1,720 − 1,600) ÷ 1,600 × 100 = +7.5%. Going back from $1,720 to $1,600 is a change of −6.98%, not −7.5%, because the starting value is different. The percent difference between the two rents is 120 ÷ 1,660 × 100 ≈ 7.23% in either direction.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 12 out of 80 is 12 ÷ 80 × 100 = 15%.
How do I calculate percent change?
Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%. A negative answer is a decrease.
What is the difference between percent change and percent difference?
Percent change has a direction: it measures how much a value moved from a starting point. Percent difference has no starting point: it divides the gap between two values by their average, so it is the same whichever order you enter them.
Why doesn't a 10% increase followed by a 10% decrease get me back to the start?
Because the second percentage is taken from a bigger number. 100 increased by 10% is 110, and 110 decreased by 10% is 99. To undo a 10% increase you need a decrease of about 9.09%.
How do I find the original number before a percentage was added?
Divide by 1 plus the percentage as a decimal. If a price including 8% tax is $54, the pre-tax price is 54 ÷ 1.08 = $50. Use the 'X is Y% of what number' mode with X = 54 and Y = 108.
Updated October 2026. Results are estimates for education, not financial or medical advice. All math runs in your browser; nothing you type is sent anywhere.